annotate curve25519-donna.c @ 848:6c69e7df3621 ecc

curve25519
author Matt Johnston <matt@ucc.asn.au>
date Fri, 08 Nov 2013 23:11:43 +0800
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children d3925ed45a85
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1 /* Copyright 2008, Google Inc.
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2 * All rights reserved.
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3 *
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4 * Redistribution and use in source and binary forms, with or without
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5 * modification, are permitted provided that the following conditions are
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6 * met:
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7 *
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8 * * Redistributions of source code must retain the above copyright
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9 * notice, this list of conditions and the following disclaimer.
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10 * * Redistributions in binary form must reproduce the above
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11 * copyright notice, this list of conditions and the following disclaimer
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12 * in the documentation and/or other materials provided with the
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13 * distribution.
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14 * * Neither the name of Google Inc. nor the names of its
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15 * contributors may be used to endorse or promote products derived from
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16 * this software without specific prior written permission.
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17 *
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18 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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19 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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20 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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21 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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22 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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23 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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24 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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25 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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26 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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27 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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28 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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29 *
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30 * curve25519-donna: Curve25519 elliptic curve, public key function
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31 *
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32 * http://code.google.com/p/curve25519-donna/
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33 *
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34 * Adam Langley <[email protected]>
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35 *
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36 * Derived from public domain C code by Daniel J. Bernstein <[email protected]>
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37 *
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38 * More information about curve25519 can be found here
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39 * http://cr.yp.to/ecdh.html
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40 *
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41 * djb's sample implementation of curve25519 is written in a special assembly
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42 * language called qhasm and uses the floating point registers.
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43 *
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44 * This is, almost, a clean room reimplementation from the curve25519 paper. It
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45 * uses many of the tricks described therein. Only the crecip function is taken
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46 * from the sample implementation.
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47 */
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48
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49 #include <string.h>
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50 #include <stdint.h>
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51
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52 #ifdef _MSC_VER
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53 #define inline __inline
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54 #endif
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55
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56 typedef uint8_t u8;
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57 typedef int32_t s32;
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58 typedef int64_t limb;
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59
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60 /* Field element representation:
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61 *
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62 * Field elements are written as an array of signed, 64-bit limbs, least
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63 * significant first. The value of the field element is:
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64 * x[0] + 2^26·x[1] + x^51·x[2] + 2^102·x[3] + ...
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65 *
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66 * i.e. the limbs are 26, 25, 26, 25, ... bits wide.
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67 */
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68
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69 /* Sum two numbers: output += in */
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70 static void fsum(limb *output, const limb *in) {
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71 unsigned i;
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72 for (i = 0; i < 10; i += 2) {
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73 output[0+i] = (output[0+i] + in[0+i]);
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74 output[1+i] = (output[1+i] + in[1+i]);
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75 }
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76 }
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77
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78 /* Find the difference of two numbers: output = in - output
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79 * (note the order of the arguments!)
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80 */
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81 static void fdifference(limb *output, const limb *in) {
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82 unsigned i;
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83 for (i = 0; i < 10; ++i) {
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84 output[i] = (in[i] - output[i]);
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85 }
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86 }
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87
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88 /* Multiply a number by a scalar: output = in * scalar */
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89 static void fscalar_product(limb *output, const limb *in, const limb scalar) {
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90 unsigned i;
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91 for (i = 0; i < 10; ++i) {
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92 output[i] = in[i] * scalar;
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93 }
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94 }
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95
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96 /* Multiply two numbers: output = in2 * in
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97 *
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98 * output must be distinct to both inputs. The inputs are reduced coefficient
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99 * form, the output is not.
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100 */
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101 static void fproduct(limb *output, const limb *in2, const limb *in) {
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102 output[0] = ((limb) ((s32) in2[0])) * ((s32) in[0]);
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103 output[1] = ((limb) ((s32) in2[0])) * ((s32) in[1]) +
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104 ((limb) ((s32) in2[1])) * ((s32) in[0]);
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105 output[2] = 2 * ((limb) ((s32) in2[1])) * ((s32) in[1]) +
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106 ((limb) ((s32) in2[0])) * ((s32) in[2]) +
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107 ((limb) ((s32) in2[2])) * ((s32) in[0]);
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108 output[3] = ((limb) ((s32) in2[1])) * ((s32) in[2]) +
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109 ((limb) ((s32) in2[2])) * ((s32) in[1]) +
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110 ((limb) ((s32) in2[0])) * ((s32) in[3]) +
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111 ((limb) ((s32) in2[3])) * ((s32) in[0]);
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112 output[4] = ((limb) ((s32) in2[2])) * ((s32) in[2]) +
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113 2 * (((limb) ((s32) in2[1])) * ((s32) in[3]) +
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114 ((limb) ((s32) in2[3])) * ((s32) in[1])) +
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115 ((limb) ((s32) in2[0])) * ((s32) in[4]) +
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116 ((limb) ((s32) in2[4])) * ((s32) in[0]);
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117 output[5] = ((limb) ((s32) in2[2])) * ((s32) in[3]) +
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118 ((limb) ((s32) in2[3])) * ((s32) in[2]) +
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119 ((limb) ((s32) in2[1])) * ((s32) in[4]) +
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120 ((limb) ((s32) in2[4])) * ((s32) in[1]) +
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121 ((limb) ((s32) in2[0])) * ((s32) in[5]) +
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122 ((limb) ((s32) in2[5])) * ((s32) in[0]);
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123 output[6] = 2 * (((limb) ((s32) in2[3])) * ((s32) in[3]) +
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124 ((limb) ((s32) in2[1])) * ((s32) in[5]) +
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125 ((limb) ((s32) in2[5])) * ((s32) in[1])) +
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126 ((limb) ((s32) in2[2])) * ((s32) in[4]) +
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127 ((limb) ((s32) in2[4])) * ((s32) in[2]) +
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128 ((limb) ((s32) in2[0])) * ((s32) in[6]) +
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129 ((limb) ((s32) in2[6])) * ((s32) in[0]);
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130 output[7] = ((limb) ((s32) in2[3])) * ((s32) in[4]) +
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131 ((limb) ((s32) in2[4])) * ((s32) in[3]) +
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132 ((limb) ((s32) in2[2])) * ((s32) in[5]) +
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133 ((limb) ((s32) in2[5])) * ((s32) in[2]) +
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134 ((limb) ((s32) in2[1])) * ((s32) in[6]) +
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135 ((limb) ((s32) in2[6])) * ((s32) in[1]) +
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136 ((limb) ((s32) in2[0])) * ((s32) in[7]) +
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137 ((limb) ((s32) in2[7])) * ((s32) in[0]);
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138 output[8] = ((limb) ((s32) in2[4])) * ((s32) in[4]) +
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139 2 * (((limb) ((s32) in2[3])) * ((s32) in[5]) +
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140 ((limb) ((s32) in2[5])) * ((s32) in[3]) +
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141 ((limb) ((s32) in2[1])) * ((s32) in[7]) +
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142 ((limb) ((s32) in2[7])) * ((s32) in[1])) +
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143 ((limb) ((s32) in2[2])) * ((s32) in[6]) +
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144 ((limb) ((s32) in2[6])) * ((s32) in[2]) +
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145 ((limb) ((s32) in2[0])) * ((s32) in[8]) +
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146 ((limb) ((s32) in2[8])) * ((s32) in[0]);
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147 output[9] = ((limb) ((s32) in2[4])) * ((s32) in[5]) +
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148 ((limb) ((s32) in2[5])) * ((s32) in[4]) +
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149 ((limb) ((s32) in2[3])) * ((s32) in[6]) +
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diff changeset
150 ((limb) ((s32) in2[6])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
151 ((limb) ((s32) in2[2])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
152 ((limb) ((s32) in2[7])) * ((s32) in[2]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
153 ((limb) ((s32) in2[1])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
154 ((limb) ((s32) in2[8])) * ((s32) in[1]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
155 ((limb) ((s32) in2[0])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
156 ((limb) ((s32) in2[9])) * ((s32) in[0]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
157 output[10] = 2 * (((limb) ((s32) in2[5])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
158 ((limb) ((s32) in2[3])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
159 ((limb) ((s32) in2[7])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
160 ((limb) ((s32) in2[1])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
161 ((limb) ((s32) in2[9])) * ((s32) in[1])) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
162 ((limb) ((s32) in2[4])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
163 ((limb) ((s32) in2[6])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
164 ((limb) ((s32) in2[2])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
165 ((limb) ((s32) in2[8])) * ((s32) in[2]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
166 output[11] = ((limb) ((s32) in2[5])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
167 ((limb) ((s32) in2[6])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
168 ((limb) ((s32) in2[4])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
169 ((limb) ((s32) in2[7])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
170 ((limb) ((s32) in2[3])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
171 ((limb) ((s32) in2[8])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
172 ((limb) ((s32) in2[2])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
173 ((limb) ((s32) in2[9])) * ((s32) in[2]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
174 output[12] = ((limb) ((s32) in2[6])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
175 2 * (((limb) ((s32) in2[5])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
176 ((limb) ((s32) in2[7])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
177 ((limb) ((s32) in2[3])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
178 ((limb) ((s32) in2[9])) * ((s32) in[3])) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
179 ((limb) ((s32) in2[4])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
180 ((limb) ((s32) in2[8])) * ((s32) in[4]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
181 output[13] = ((limb) ((s32) in2[6])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
182 ((limb) ((s32) in2[7])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
183 ((limb) ((s32) in2[5])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
184 ((limb) ((s32) in2[8])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
185 ((limb) ((s32) in2[4])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
186 ((limb) ((s32) in2[9])) * ((s32) in[4]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
187 output[14] = 2 * (((limb) ((s32) in2[7])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
188 ((limb) ((s32) in2[5])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
189 ((limb) ((s32) in2[9])) * ((s32) in[5])) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
190 ((limb) ((s32) in2[6])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
191 ((limb) ((s32) in2[8])) * ((s32) in[6]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
192 output[15] = ((limb) ((s32) in2[7])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
193 ((limb) ((s32) in2[8])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
194 ((limb) ((s32) in2[6])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
195 ((limb) ((s32) in2[9])) * ((s32) in[6]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
196 output[16] = ((limb) ((s32) in2[8])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
197 2 * (((limb) ((s32) in2[7])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
198 ((limb) ((s32) in2[9])) * ((s32) in[7]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
199 output[17] = ((limb) ((s32) in2[8])) * ((s32) in[9]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
200 ((limb) ((s32) in2[9])) * ((s32) in[8]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
201 output[18] = 2 * ((limb) ((s32) in2[9])) * ((s32) in[9]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
202 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
203
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
204 /* Reduce a long form to a short form by taking the input mod 2^255 - 19. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
205 static void freduce_degree(limb *output) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
206 /* Each of these shifts and adds ends up multiplying the value by 19. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
207 output[8] += output[18] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
208 output[8] += output[18] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
209 output[8] += output[18];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
210 output[7] += output[17] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
211 output[7] += output[17] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
212 output[7] += output[17];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
213 output[6] += output[16] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
214 output[6] += output[16] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
215 output[6] += output[16];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
216 output[5] += output[15] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
217 output[5] += output[15] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
218 output[5] += output[15];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
219 output[4] += output[14] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
220 output[4] += output[14] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
221 output[4] += output[14];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
222 output[3] += output[13] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
223 output[3] += output[13] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
224 output[3] += output[13];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
225 output[2] += output[12] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
226 output[2] += output[12] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
227 output[2] += output[12];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
228 output[1] += output[11] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
229 output[1] += output[11] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
230 output[1] += output[11];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
231 output[0] += output[10] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
232 output[0] += output[10] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
233 output[0] += output[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
234 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
235
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
236 #if (-1 & 3) != 3
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
237 #error "This code only works on a two's complement system"
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
238 #endif
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
239
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
240 /* return v / 2^26, using only shifts and adds. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
241 static inline limb
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
242 div_by_2_26(const limb v)
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
243 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
244 /* High word of v; no shift needed*/
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
245 const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
246 /* Set to all 1s if v was negative; else set to 0s. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
247 const int32_t sign = ((int32_t) highword) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
248 /* Set to 0x3ffffff if v was negative; else set to 0. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
249 const int32_t roundoff = ((uint32_t) sign) >> 6;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
250 /* Should return v / (1<<26) */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
251 return (v + roundoff) >> 26;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
252 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
253
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
254 /* return v / (2^25), using only shifts and adds. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
255 static inline limb
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
256 div_by_2_25(const limb v)
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
257 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
258 /* High word of v; no shift needed*/
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
259 const uint32_t highword = (uint32_t) (((uint64_t) v) >> 32);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
260 /* Set to all 1s if v was negative; else set to 0s. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
261 const int32_t sign = ((int32_t) highword) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
262 /* Set to 0x1ffffff if v was negative; else set to 0. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
263 const int32_t roundoff = ((uint32_t) sign) >> 7;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
264 /* Should return v / (1<<25) */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
265 return (v + roundoff) >> 25;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
266 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
267
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
268 static inline s32
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
269 div_s32_by_2_25(const s32 v)
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
270 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
271 const s32 roundoff = ((uint32_t)(v >> 31)) >> 7;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
272 return (v + roundoff) >> 25;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
273 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
274
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
275 /* Reduce all coefficients of the short form input so that |x| < 2^26.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
276 *
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
277 * On entry: |output[i]| < 2^62
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
278 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
279 static void freduce_coefficients(limb *output) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
280 unsigned i;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
281
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
282 output[10] = 0;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
283
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
284 for (i = 0; i < 10; i += 2) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
285 limb over = div_by_2_26(output[i]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
286 output[i] -= over << 26;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
287 output[i+1] += over;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
288
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
289 over = div_by_2_25(output[i+1]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
290 output[i+1] -= over << 25;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
291 output[i+2] += over;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
292 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
293 /* Now |output[10]| < 2 ^ 38 and all other coefficients are reduced. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
294 output[0] += output[10] << 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
295 output[0] += output[10] << 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
296 output[0] += output[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
297
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
298 output[10] = 0;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
299
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
300 /* Now output[1..9] are reduced, and |output[0]| < 2^26 + 19 * 2^38
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
301 * So |over| will be no more than 77825 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
302 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
303 limb over = div_by_2_26(output[0]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
304 output[0] -= over << 26;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
305 output[1] += over;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
306 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
307
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
308 /* Now output[0,2..9] are reduced, and |output[1]| < 2^25 + 77825
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
309 * So |over| will be no more than 1. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
310 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
311 /* output[1] fits in 32 bits, so we can use div_s32_by_2_25 here. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
312 s32 over32 = div_s32_by_2_25((s32) output[1]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
313 output[1] -= over32 << 25;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
314 output[2] += over32;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
315 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
316
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
317 /* Finally, output[0,1,3..9] are reduced, and output[2] is "nearly reduced":
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
318 * we have |output[2]| <= 2^26. This is good enough for all of our math,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
319 * but it will require an extra freduce_coefficients before fcontract. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
320 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
321
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
322 /* A helpful wrapper around fproduct: output = in * in2.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
323 *
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
324 * output must be distinct to both inputs. The output is reduced degree and
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
325 * reduced coefficient.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
326 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
327 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
328 fmul(limb *output, const limb *in, const limb *in2) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
329 limb t[19];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
330 fproduct(t, in, in2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
331 freduce_degree(t);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
332 freduce_coefficients(t);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
333 memcpy(output, t, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
334 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
335
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
336 static void fsquare_inner(limb *output, const limb *in) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
337 output[0] = ((limb) ((s32) in[0])) * ((s32) in[0]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
338 output[1] = 2 * ((limb) ((s32) in[0])) * ((s32) in[1]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
339 output[2] = 2 * (((limb) ((s32) in[1])) * ((s32) in[1]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
340 ((limb) ((s32) in[0])) * ((s32) in[2]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
341 output[3] = 2 * (((limb) ((s32) in[1])) * ((s32) in[2]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
342 ((limb) ((s32) in[0])) * ((s32) in[3]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
343 output[4] = ((limb) ((s32) in[2])) * ((s32) in[2]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
344 4 * ((limb) ((s32) in[1])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
345 2 * ((limb) ((s32) in[0])) * ((s32) in[4]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
346 output[5] = 2 * (((limb) ((s32) in[2])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
347 ((limb) ((s32) in[1])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
348 ((limb) ((s32) in[0])) * ((s32) in[5]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
349 output[6] = 2 * (((limb) ((s32) in[3])) * ((s32) in[3]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
350 ((limb) ((s32) in[2])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
351 ((limb) ((s32) in[0])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
352 2 * ((limb) ((s32) in[1])) * ((s32) in[5]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
353 output[7] = 2 * (((limb) ((s32) in[3])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
354 ((limb) ((s32) in[2])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
355 ((limb) ((s32) in[1])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
356 ((limb) ((s32) in[0])) * ((s32) in[7]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
357 output[8] = ((limb) ((s32) in[4])) * ((s32) in[4]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
358 2 * (((limb) ((s32) in[2])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
359 ((limb) ((s32) in[0])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
360 2 * (((limb) ((s32) in[1])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
361 ((limb) ((s32) in[3])) * ((s32) in[5])));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
362 output[9] = 2 * (((limb) ((s32) in[4])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
363 ((limb) ((s32) in[3])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
364 ((limb) ((s32) in[2])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
365 ((limb) ((s32) in[1])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
366 ((limb) ((s32) in[0])) * ((s32) in[9]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
367 output[10] = 2 * (((limb) ((s32) in[5])) * ((s32) in[5]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
368 ((limb) ((s32) in[4])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
369 ((limb) ((s32) in[2])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
370 2 * (((limb) ((s32) in[3])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
371 ((limb) ((s32) in[1])) * ((s32) in[9])));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
372 output[11] = 2 * (((limb) ((s32) in[5])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
373 ((limb) ((s32) in[4])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
374 ((limb) ((s32) in[3])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
375 ((limb) ((s32) in[2])) * ((s32) in[9]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
376 output[12] = ((limb) ((s32) in[6])) * ((s32) in[6]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
377 2 * (((limb) ((s32) in[4])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
378 2 * (((limb) ((s32) in[5])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
379 ((limb) ((s32) in[3])) * ((s32) in[9])));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
380 output[13] = 2 * (((limb) ((s32) in[6])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
381 ((limb) ((s32) in[5])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
382 ((limb) ((s32) in[4])) * ((s32) in[9]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
383 output[14] = 2 * (((limb) ((s32) in[7])) * ((s32) in[7]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
384 ((limb) ((s32) in[6])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
385 2 * ((limb) ((s32) in[5])) * ((s32) in[9]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
386 output[15] = 2 * (((limb) ((s32) in[7])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
387 ((limb) ((s32) in[6])) * ((s32) in[9]));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
388 output[16] = ((limb) ((s32) in[8])) * ((s32) in[8]) +
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
389 4 * ((limb) ((s32) in[7])) * ((s32) in[9]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
390 output[17] = 2 * ((limb) ((s32) in[8])) * ((s32) in[9]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
391 output[18] = 2 * ((limb) ((s32) in[9])) * ((s32) in[9]);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
392 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
393
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
394 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
395 fsquare(limb *output, const limb *in) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
396 limb t[19];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
397 fsquare_inner(t, in);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
398 freduce_degree(t);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
399 freduce_coefficients(t);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
400 memcpy(output, t, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
401 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
402
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
403 /* Take a little-endian, 32-byte number and expand it into polynomial form */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
404 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
405 fexpand(limb *output, const u8 *input) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
406 #define F(n,start,shift,mask) \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
407 output[n] = ((((limb) input[start + 0]) | \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
408 ((limb) input[start + 1]) << 8 | \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
409 ((limb) input[start + 2]) << 16 | \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
410 ((limb) input[start + 3]) << 24) >> shift) & mask;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
411 F(0, 0, 0, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
412 F(1, 3, 2, 0x1ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
413 F(2, 6, 3, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
414 F(3, 9, 5, 0x1ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
415 F(4, 12, 6, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
416 F(5, 16, 0, 0x1ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
417 F(6, 19, 1, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
418 F(7, 22, 3, 0x1ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
419 F(8, 25, 4, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
420 F(9, 28, 6, 0x3ffffff);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
421 #undef F
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
422 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
423
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
424 #if (-32 >> 1) != -16
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
425 #error "This code only works when >> does sign-extension on negative numbers"
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
426 #endif
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
427
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
428 /* Take a fully reduced polynomial form number and contract it into a
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
429 * little-endian, 32-byte array
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
430 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
431 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
432 fcontract(u8 *output, limb *input) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
433 int i;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
434 int j;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
435
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
436 for (j = 0; j < 2; ++j) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
437 for (i = 0; i < 9; ++i) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
438 if ((i & 1) == 1) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
439 /* This calculation is a time-invariant way to make input[i] positive
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
440 by borrowing from the next-larger limb.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
441 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
442 const s32 mask = (s32)(input[i]) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
443 const s32 carry = -(((s32)(input[i]) & mask) >> 25);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
444 input[i] = (s32)(input[i]) + (carry << 25);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
445 input[i+1] = (s32)(input[i+1]) - carry;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
446 } else {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
447 const s32 mask = (s32)(input[i]) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
448 const s32 carry = -(((s32)(input[i]) & mask) >> 26);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
449 input[i] = (s32)(input[i]) + (carry << 26);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
450 input[i+1] = (s32)(input[i+1]) - carry;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
451 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
452 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
453 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
454 const s32 mask = (s32)(input[9]) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
455 const s32 carry = -(((s32)(input[9]) & mask) >> 25);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
456 input[9] = (s32)(input[9]) + (carry << 25);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
457 input[0] = (s32)(input[0]) - (carry * 19);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
458 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
459 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
460
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
461 /* The first borrow-propagation pass above ended with every limb
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
462 except (possibly) input[0] non-negative.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
463
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
464 Since each input limb except input[0] is decreased by at most 1
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
465 by a borrow-propagation pass, the second borrow-propagation pass
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
466 could only have wrapped around to decrease input[0] again if the
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
467 first pass left input[0] negative *and* input[1] through input[9]
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
468 were all zero. In that case, input[1] is now 2^25 - 1, and this
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
469 last borrow-propagation step will leave input[1] non-negative.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
470 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
471 {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
472 const s32 mask = (s32)(input[0]) >> 31;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
473 const s32 carry = -(((s32)(input[0]) & mask) >> 26);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
474 input[0] = (s32)(input[0]) + (carry << 26);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
475 input[1] = (s32)(input[1]) - carry;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
476 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
477
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
478 /* Both passes through the above loop, plus the last 0-to-1 step, are
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
479 necessary: if input[9] is -1 and input[0] through input[8] are 0,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
480 negative values will remain in the array until the end.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
481 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
482
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
483 input[1] <<= 2;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
484 input[2] <<= 3;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
485 input[3] <<= 5;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
486 input[4] <<= 6;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
487 input[6] <<= 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
488 input[7] <<= 3;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
489 input[8] <<= 4;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
490 input[9] <<= 6;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
491 #define F(i, s) \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
492 output[s+0] |= input[i] & 0xff; \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
493 output[s+1] = (input[i] >> 8) & 0xff; \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
494 output[s+2] = (input[i] >> 16) & 0xff; \
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
495 output[s+3] = (input[i] >> 24) & 0xff;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
496 output[0] = 0;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
497 output[16] = 0;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
498 F(0,0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
499 F(1,3);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
500 F(2,6);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
501 F(3,9);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
502 F(4,12);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
503 F(5,16);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
504 F(6,19);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
505 F(7,22);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
506 F(8,25);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
507 F(9,28);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
508 #undef F
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
509 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
510
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
511 /* Input: Q, Q', Q-Q'
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
512 * Output: 2Q, Q+Q'
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
513 *
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
514 * x2 z3: long form
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
515 * x3 z3: long form
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
516 * x z: short form, destroyed
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
517 * xprime zprime: short form, destroyed
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
518 * qmqp: short form, preserved
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
519 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
520 static void fmonty(limb *x2, limb *z2, /* output 2Q */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
521 limb *x3, limb *z3, /* output Q + Q' */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
522 limb *x, limb *z, /* input Q */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
523 limb *xprime, limb *zprime, /* input Q' */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
524 const limb *qmqp /* input Q - Q' */) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
525 limb origx[10], origxprime[10], zzz[19], xx[19], zz[19], xxprime[19],
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
526 zzprime[19], zzzprime[19], xxxprime[19];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
527
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
528 memcpy(origx, x, 10 * sizeof(limb));
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
529 fsum(x, z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
530 fdifference(z, origx); // does x - z
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
531
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
532 memcpy(origxprime, xprime, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
533 fsum(xprime, zprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
534 fdifference(zprime, origxprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
535 fproduct(xxprime, xprime, z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
536 fproduct(zzprime, x, zprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
537 freduce_degree(xxprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
538 freduce_coefficients(xxprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
539 freduce_degree(zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
540 freduce_coefficients(zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
541 memcpy(origxprime, xxprime, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
542 fsum(xxprime, zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
543 fdifference(zzprime, origxprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
544 fsquare(xxxprime, xxprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
545 fsquare(zzzprime, zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
546 fproduct(zzprime, zzzprime, qmqp);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
547 freduce_degree(zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
548 freduce_coefficients(zzprime);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
549 memcpy(x3, xxxprime, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
550 memcpy(z3, zzprime, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
551
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
552 fsquare(xx, x);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
553 fsquare(zz, z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
554 fproduct(x2, xx, zz);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
555 freduce_degree(x2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
556 freduce_coefficients(x2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
557 fdifference(zz, xx); // does zz = xx - zz
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
558 memset(zzz + 10, 0, sizeof(limb) * 9);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
559 fscalar_product(zzz, zz, 121665);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
560 /* No need to call freduce_degree here:
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
561 fscalar_product doesn't increase the degree of its input. */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
562 freduce_coefficients(zzz);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
563 fsum(zzz, xx);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
564 fproduct(z2, zz, zzz);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
565 freduce_degree(z2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
566 freduce_coefficients(z2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
567 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
568
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
569 /* Conditionally swap two reduced-form limb arrays if 'iswap' is 1, but leave
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
570 * them unchanged if 'iswap' is 0. Runs in data-invariant time to avoid
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
571 * side-channel attacks.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
572 *
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
573 * NOTE that this function requires that 'iswap' be 1 or 0; other values give
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
574 * wrong results. Also, the two limb arrays must be in reduced-coefficient,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
575 * reduced-degree form: the values in a[10..19] or b[10..19] aren't swapped,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
576 * and all all values in a[0..9],b[0..9] must have magnitude less than
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
577 * INT32_MAX.
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
578 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
579 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
580 swap_conditional(limb a[19], limb b[19], limb iswap) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
581 unsigned i;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
582 const s32 swap = (s32) -iswap;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
583
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
584 for (i = 0; i < 10; ++i) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
585 const s32 x = swap & ( ((s32)a[i]) ^ ((s32)b[i]) );
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
586 a[i] = ((s32)a[i]) ^ x;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
587 b[i] = ((s32)b[i]) ^ x;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
588 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
589 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
590
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
591 /* Calculates nQ where Q is the x-coordinate of a point on the curve
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
592 *
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
593 * resultx/resultz: the x coordinate of the resulting curve point (short form)
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
594 * n: a little endian, 32-byte number
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
595 * q: a point of the curve (short form)
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
596 */
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
597 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
598 cmult(limb *resultx, limb *resultz, const u8 *n, const limb *q) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
599 limb a[19] = {0}, b[19] = {1}, c[19] = {1}, d[19] = {0};
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
600 limb *nqpqx = a, *nqpqz = b, *nqx = c, *nqz = d, *t;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
601 limb e[19] = {0}, f[19] = {1}, g[19] = {0}, h[19] = {1};
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
602 limb *nqpqx2 = e, *nqpqz2 = f, *nqx2 = g, *nqz2 = h;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
603
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
604 unsigned i, j;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
605
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
606 memcpy(nqpqx, q, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
607
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
608 for (i = 0; i < 32; ++i) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
609 u8 byte = n[31 - i];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
610 for (j = 0; j < 8; ++j) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
611 const limb bit = byte >> 7;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
612
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
613 swap_conditional(nqx, nqpqx, bit);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
614 swap_conditional(nqz, nqpqz, bit);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
615 fmonty(nqx2, nqz2,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
616 nqpqx2, nqpqz2,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
617 nqx, nqz,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
618 nqpqx, nqpqz,
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
619 q);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
620 swap_conditional(nqx2, nqpqx2, bit);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
621 swap_conditional(nqz2, nqpqz2, bit);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
622
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
623 t = nqx;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
624 nqx = nqx2;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
625 nqx2 = t;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
626 t = nqz;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
627 nqz = nqz2;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
628 nqz2 = t;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
629 t = nqpqx;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
630 nqpqx = nqpqx2;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
631 nqpqx2 = t;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
632 t = nqpqz;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
633 nqpqz = nqpqz2;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
634 nqpqz2 = t;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
635
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
636 byte <<= 1;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
637 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
638 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
639
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
640 memcpy(resultx, nqx, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
641 memcpy(resultz, nqz, sizeof(limb) * 10);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
642 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
643
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
644 // -----------------------------------------------------------------------------
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
645 // Shamelessly copied from djb's code
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
646 // -----------------------------------------------------------------------------
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
647 static void
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
648 crecip(limb *out, const limb *z) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
649 limb z2[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
650 limb z9[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
651 limb z11[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
652 limb z2_5_0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
653 limb z2_10_0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
654 limb z2_20_0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
655 limb z2_50_0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
656 limb z2_100_0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
657 limb t0[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
658 limb t1[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
659 int i;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
660
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
661 /* 2 */ fsquare(z2,z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
662 /* 4 */ fsquare(t1,z2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
663 /* 8 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
664 /* 9 */ fmul(z9,t0,z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
665 /* 11 */ fmul(z11,z9,z2);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
666 /* 22 */ fsquare(t0,z11);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
667 /* 2^5 - 2^0 = 31 */ fmul(z2_5_0,t0,z9);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
668
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
669 /* 2^6 - 2^1 */ fsquare(t0,z2_5_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
670 /* 2^7 - 2^2 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
671 /* 2^8 - 2^3 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
672 /* 2^9 - 2^4 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
673 /* 2^10 - 2^5 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
674 /* 2^10 - 2^0 */ fmul(z2_10_0,t0,z2_5_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
675
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
676 /* 2^11 - 2^1 */ fsquare(t0,z2_10_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
677 /* 2^12 - 2^2 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
678 /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
679 /* 2^20 - 2^0 */ fmul(z2_20_0,t1,z2_10_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
680
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
681 /* 2^21 - 2^1 */ fsquare(t0,z2_20_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
682 /* 2^22 - 2^2 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
683 /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
684 /* 2^40 - 2^0 */ fmul(t0,t1,z2_20_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
685
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
686 /* 2^41 - 2^1 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
687 /* 2^42 - 2^2 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
688 /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
689 /* 2^50 - 2^0 */ fmul(z2_50_0,t0,z2_10_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
690
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
691 /* 2^51 - 2^1 */ fsquare(t0,z2_50_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
692 /* 2^52 - 2^2 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
693 /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
694 /* 2^100 - 2^0 */ fmul(z2_100_0,t1,z2_50_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
695
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
696 /* 2^101 - 2^1 */ fsquare(t1,z2_100_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
697 /* 2^102 - 2^2 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
698 /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fsquare(t1,t0); fsquare(t0,t1); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
699 /* 2^200 - 2^0 */ fmul(t1,t0,z2_100_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
700
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
701 /* 2^201 - 2^1 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
702 /* 2^202 - 2^2 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
703 /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fsquare(t0,t1); fsquare(t1,t0); }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
704 /* 2^250 - 2^0 */ fmul(t0,t1,z2_50_0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
705
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
706 /* 2^251 - 2^1 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
707 /* 2^252 - 2^2 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
708 /* 2^253 - 2^3 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
709 /* 2^254 - 2^4 */ fsquare(t0,t1);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
710 /* 2^255 - 2^5 */ fsquare(t1,t0);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
711 /* 2^255 - 21 */ fmul(out,t1,z11);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
712 }
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
713
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
714 int curve25519_donna(u8 *, const u8 *, const u8 *);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
715
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
716 int
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
717 curve25519_donna(u8 *mypublic, const u8 *secret, const u8 *basepoint) {
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
718 limb bp[10], x[10], z[11], zmone[10];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
719 uint8_t e[32];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
720 int i;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
721
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
722 for (i = 0; i < 32; ++i) e[i] = secret[i];
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
723 e[0] &= 248;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
724 e[31] &= 127;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
725 e[31] |= 64;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
726
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
727 fexpand(bp, basepoint);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
728 cmult(x, z, e, bp);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
729 crecip(zmone, z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
730 fmul(z, x, zmone);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
731 freduce_coefficients(z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
732 fcontract(mypublic, z);
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
733 return 0;
6c69e7df3621 curve25519
Matt Johnston <matt@ucc.asn.au>
parents:
diff changeset
734 }